Descriptive and Data Exploration

Mechanical properties by raw material

ggplot(combined, aes(Raw.Material, ymodule)) + geom_point(aes(color=Raw.Material)) + ylab("Young's Modulus") + xlab("Raw Material") + ggtitle("Young's Modulus")

ggplot(combined, aes(Raw.Material, Leeb.Hardness)) + geom_point(aes(color=Raw.Material)) + xlab("Raw Material") + ylab("Leeb Harndess") + ggtitle("Leeb's Hardness") + theme(legend.title = element_text(colour="blue", size=15, face="bold"),legend.text = element_text(colour="red", size = 10, face = "bold"))

Subset by raw material

granite<-subset(combined, combined$Raw.Material=="granite")
rhyolite<-subset(combined, combined$Raw.Material=="rhyolite")
dacite<-subset(combined, combined$Raw.Material=="dacite")
fenitized_gneiss<-subset(combined, combined$Raw.Material=="fenitized gneiss")
carbonatite<-subset(combined, combined$Raw.Material=="carbonatite")
quartzite<-subset(combined, combined$Raw.Material=="quartzite")

Is there a relationship between crystallinity and raw material?

ggplot(combined, aes(Raw.Material, Percent.Area)) + geom_boxplot(aes(fill=Raw.Material)) + ylab("Percent Crystal") + xlab("Raw Material") + ggtitle("Crystallinity by Raw Material") + scale_fill_discrete(name="Raw Material") + theme(legend.title = element_text(colour="blue", size=15, face="bold"),legend.text = element_text(colour="red", size = 10, face = "bold"))

Angle and raw material?

ggplot(combined, aes(Raw.Material, Angle)) + geom_boxplot(aes(fill=Raw.Material)) + ylab("Angle") + xlab("Raw Material") + ggtitle("Crystal Angularity  by Raw Material") + scale_fill_discrete(name="Raw Material") + theme(legend.title = element_text(colour="blue", size=15, face="bold"),legend.text = element_text(colour="red", size = 10, face = "bold"))

Crystal size and raw material?

ggplot(combined, aes(Raw.Material, Average.Size)) + geom_boxplot(aes(fill=Raw.Material)) + ylab("Average size") + xlab("Raw Material") + ggtitle("Average crystal size by Raw Material") + scale_fill_discrete(name="Raw Material") + theme(legend.title = element_text(colour="blue", size=15, face="bold"),legend.text = element_text(colour="red", size = 10, face = "bold"))

###Total area and raw material

ggplot(combined, aes(Raw.Material, Total.Area)) + geom_boxplot(aes(fill=Raw.Material)) + ylab("Total Area") + xlab("Raw Material") + ggtitle("Total Area by Raw Material") + scale_fill_discrete(name="Raw Material") + theme(legend.title = element_text(colour="blue", size=15, face="bold"),legend.text = element_text(colour="red", size = 10, face = "bold"))

Normality tests

Granite

shapiro.test(granite$Percent.Area)
## 
##  Shapiro-Wilk normality test
## 
## data:  granite$Percent.Area
## W = 0.99233, p-value = 0.2049
hist(granite$Percent.Area)

shapiro.test(granite$Angle)
## 
##  Shapiro-Wilk normality test
## 
## data:  granite$Angle
## W = 0.98835, p-value = 0.03605
hist(granite$Angle)

shapiro.test(granite$Average.Size)
## 
##  Shapiro-Wilk normality test
## 
## data:  granite$Average.Size
## W = 0.8806, p-value = 2.575e-13
hist(granite$Average.Size)

shapiro.test(granite$Total.Area)
## 
##  Shapiro-Wilk normality test
## 
## data:  granite$Total.Area
## W = 0.99234, p-value = 0.205
hist(granite$Total.Area)

Average crystal size for granite is not normally distributed which makes sense because granite tends to have a lot of smaller crystals and less larger crystals.

Rhyolite

shapiro.test(rhyolite$Percent.Area)
## 
##  Shapiro-Wilk normality test
## 
## data:  rhyolite$Percent.Area
## W = 0.88706, p-value < 2.2e-16
hist(rhyolite$Percent.Area)

shapiro.test(rhyolite$Angle)
## 
##  Shapiro-Wilk normality test
## 
## data:  rhyolite$Angle
## W = 0.99103, p-value = 0.0157
hist(rhyolite$Angle)

shapiro.test(rhyolite$Average.Size)
## 
##  Shapiro-Wilk normality test
## 
## data:  rhyolite$Average.Size
## W = 0.47961, p-value < 2.2e-16
hist(rhyolite$Average.Size)

shapiro.test(rhyolite$Total.Area)
## 
##  Shapiro-Wilk normality test
## 
## data:  rhyolite$Total.Area
## W = 0.88707, p-value < 2.2e-16
hist(rhyolite$Total.Area)

Carbonatite

shapiro.test(carbonatite$Percent.Area)
## 
##  Shapiro-Wilk normality test
## 
## data:  carbonatite$Percent.Area
## W = 0.98409, p-value = 0.005778
hist(carbonatite$Percent.Area)

shapiro.test(carbonatite$Angle)
## 
##  Shapiro-Wilk normality test
## 
## data:  carbonatite$Angle
## W = 0.99641, p-value = 0.8267
hist(carbonatite$Angle)

shapiro.test(carbonatite$Average.Size)
## 
##  Shapiro-Wilk normality test
## 
## data:  carbonatite$Average.Size
## W = 0.65585, p-value < 2.2e-16
hist(carbonatite$Average.Size)

shapiro.test(carbonatite$Total.Area)
## 
##  Shapiro-Wilk normality test
## 
## data:  carbonatite$Total.Area
## W = 0.98409, p-value = 0.005775
hist(carbonatite$Total.Area)

Dacite

shapiro.test(dacite$Percent.Area)
## 
##  Shapiro-Wilk normality test
## 
## data:  dacite$Percent.Area
## W = 0.96764, p-value = 3.153e-07
hist(dacite$Percent.Area)

shapiro.test(dacite$Angle)
## 
##  Shapiro-Wilk normality test
## 
## data:  dacite$Angle
## W = 0.97416, p-value = 4.336e-06
hist(dacite$Angle)

shapiro.test(dacite$Average.Size)
## 
##  Shapiro-Wilk normality test
## 
## data:  dacite$Average.Size
## W = 0.5693, p-value < 2.2e-16
hist(dacite$Average.Size)

shapiro.test(dacite$Total.Area)
## 
##  Shapiro-Wilk normality test
## 
## data:  dacite$Total.Area
## W = 0.96764, p-value = 3.152e-07
hist(dacite$Total.Area)

Quartzite

shapiro.test(quartzite$Percent.Area)
## 
##  Shapiro-Wilk normality test
## 
## data:  quartzite$Percent.Area
## W = 0.98274, p-value = 2.76e-05
hist(quartzite$Percent.Area)

shapiro.test(quartzite$Angle)
## 
##  Shapiro-Wilk normality test
## 
## data:  quartzite$Angle
## W = 0.99184, p-value = 0.01259
hist(quartzite$Angle)

shapiro.test(quartzite$Average.Size)
## 
##  Shapiro-Wilk normality test
## 
## data:  quartzite$Average.Size
## W = 0.72762, p-value < 2.2e-16
hist(quartzite$Average.Size)

shapiro.test(quartzite$Total.Area)
## 
##  Shapiro-Wilk normality test
## 
## data:  quartzite$Total.Area
## W = 0.98274, p-value = 2.76e-05
hist(quartzite$Total.Area)

Fenitized gneiss

shapiro.test(fenitized_gneiss$Percent.Area)
## 
##  Shapiro-Wilk normality test
## 
## data:  fenitized_gneiss$Percent.Area
## W = 0.97922, p-value = 0.001074
hist(fenitized_gneiss$Percent.Area)

shapiro.test(fenitized_gneiss$Angle)
## 
##  Shapiro-Wilk normality test
## 
## data:  fenitized_gneiss$Angle
## W = 0.88965, p-value = 1.798e-12
hist(fenitized_gneiss$Angle)

shapiro.test(fenitized_gneiss$Average.Size)
## 
##  Shapiro-Wilk normality test
## 
## data:  fenitized_gneiss$Average.Size
## W = 0.7299, p-value < 2.2e-16
hist(fenitized_gneiss$Average.Size)

shapiro.test(fenitized_gneiss$Total.Area)
## 
##  Shapiro-Wilk normality test
## 
## data:  fenitized_gneiss$Total.Area
## W = 0.97922, p-value = 0.001075
hist(fenitized_gneiss$Total.Area)

Non-Parametric ANOVA

kruskal.test(Percent.Area ~ Raw.Material , data=combined)
## 
##  Kruskal-Wallis rank sum test
## 
## data:  Percent.Area by Raw.Material
## Kruskal-Wallis chi-squared = 1072.6, df = 5, p-value < 2.2e-16
kruskal.test(Average.Size ~ Raw.Material , data=combined)
## 
##  Kruskal-Wallis rank sum test
## 
## data:  Average.Size by Raw.Material
## Kruskal-Wallis chi-squared = 1166.6, df = 5, p-value < 2.2e-16

crystalinity is significantly different by raw material Average size is significantly different by raw material

ANOVA ANALYSIS

leeb hardness ~ rawmaterial * Percent.crystals

Leeb_PA<-lm(combined$Leeb.Hardness ~ combined$Raw.Material * combined$Percent.Area)
Leeb_PA
## 
## Call:
## lm(formula = combined$Leeb.Hardness ~ combined$Raw.Material * 
##     combined$Percent.Area)
## 
## Coefficients:
##                                                 (Intercept)  
##                                                   2.848e+02  
##                                 combined$Raw.Materialdacite  
##                                                  -6.153e+01  
##                       combined$Raw.Materialfenitized gneiss  
##                                                  -7.376e+01  
##                                combined$Raw.Materialgranite  
##                                                  -1.216e+02  
##                              combined$Raw.Materialquartzite  
##                                                  -1.058e+02  
##                               combined$Raw.Materialrhyolite  
##                                                  -1.008e+02  
##                                       combined$Percent.Area  
##                                                  -8.024e-14  
##           combined$Raw.Materialdacite:combined$Percent.Area  
##                                                   8.024e-14  
## combined$Raw.Materialfenitized gneiss:combined$Percent.Area  
##                                                   8.024e-14  
##          combined$Raw.Materialgranite:combined$Percent.Area  
##                                                   8.024e-14  
##        combined$Raw.Materialquartzite:combined$Percent.Area  
##                                                   8.024e-14  
##         combined$Raw.Materialrhyolite:combined$Percent.Area  
##                                                   8.024e-14
pander(anova(Leeb_PA))
## Warning in anova.lm(Leeb_PA): ANOVA F-tests on an essentially perfect fit
## are unreliable
Analysis of Variance Table (continued below)
  Df Sum Sq Mean Sq
combined$Raw.Material 5 2701732 540346
combined$Percent.Area 1 4.757e-23 4.757e-23
combined\(Raw.Material:combined\)Percent.Area 5 1.367e-22 2.735e-23
Residuals 1974 1.438e-19 7.284e-23
  F value Pr(>F)
combined$Raw.Material 7.418e+27 0
combined$Percent.Area 0.653 0.4191
combined\(Raw.Material:combined\)Percent.Area 0.3755 0.8658
Residuals NA NA 
Leeb_PA_plot<-ggplot(combined, aes(y=Percent.Area , x=Leeb.Hardness , fill=Raw.Material)) + geom_boxplot() + ylab("Percent Area") + xlab("Leeb Hardness") + ggtitle("Leeb hardness by Raw material with Percent Crystal")

Leeb_PA_plot

leeb hardness ~ rawmaterial * total area

Leeb_TotalA<-lm(combined$Leeb.Hardness ~ combined$Raw.Material *combined$Total.Area)
Leeb_TotalA
## 
## Call:
## lm(formula = combined$Leeb.Hardness ~ combined$Raw.Material * 
##     combined$Total.Area)
## 
## Coefficients:
##                                               (Intercept)  
##                                                 2.848e+02  
##                               combined$Raw.Materialdacite  
##                                                -6.153e+01  
##                     combined$Raw.Materialfenitized gneiss  
##                                                -7.376e+01  
##                              combined$Raw.Materialgranite  
##                                                -1.216e+02  
##                            combined$Raw.Materialquartzite  
##                                                -1.058e+02  
##                             combined$Raw.Materialrhyolite  
##                                                -1.008e+02  
##                                       combined$Total.Area  
##                                                -1.087e-13  
##           combined$Raw.Materialdacite:combined$Total.Area  
##                                                 1.087e-13  
## combined$Raw.Materialfenitized gneiss:combined$Total.Area  
##                                                 1.087e-13  
##          combined$Raw.Materialgranite:combined$Total.Area  
##                                                 1.087e-13  
##        combined$Raw.Materialquartzite:combined$Total.Area  
##                                                 1.087e-13  
##         combined$Raw.Materialrhyolite:combined$Total.Area  
##                                                 1.087e-13
pander(anova(Leeb_TotalA))
## Warning in anova.lm(Leeb_TotalA): ANOVA F-tests on an essentially perfect
## fit are unreliable
Analysis of Variance Table (continued below)
  Df Sum Sq Mean Sq
combined$Raw.Material 5 2701732 540346
combined$Total.Area 1 4.758e-23 4.758e-23
combined\(Raw.Material:combined\)Total.Area 5 1.368e-22 2.735e-23
Residuals 1974 1.438e-19 7.284e-23
  F value Pr(>F)
combined$Raw.Material 7.418e+27 0
combined$Total.Area 0.6531 0.4191
combined\(Raw.Material:combined\)Total.Area 0.3755 0.8657
Residuals NA NA 
Leeb_TotalA_plot<-ggplot(combined, aes(y=Total.Area , x=Leeb.Hardness , fill=Raw.Material)) + geom_boxplot() + ylab("Total Area") + xlab("Leeb Hardness") + ggtitle("Leeb hardness by Raw material with Total Area")

Leeb_TotalA_plot

leeb hardness ~ rawmaterial * average size

Leeb_AveSize<-lm(combined$Leeb.Hardness ~ combined$Raw.Material *combined$Average.Size)
Leeb_AveSize
## 
## Call:
## lm(formula = combined$Leeb.Hardness ~ combined$Raw.Material * 
##     combined$Average.Size)
## 
## Coefficients:
##                                                 (Intercept)  
##                                                   2.848e+02  
##                                 combined$Raw.Materialdacite  
##                                                  -6.153e+01  
##                       combined$Raw.Materialfenitized gneiss  
##                                                  -7.376e+01  
##                                combined$Raw.Materialgranite  
##                                                  -1.216e+02  
##                              combined$Raw.Materialquartzite  
##                                                  -1.058e+02  
##                               combined$Raw.Materialrhyolite  
##                                                  -1.008e+02  
##                                       combined$Average.Size  
##                                                  -9.128e-12  
##           combined$Raw.Materialdacite:combined$Average.Size  
##                                                   9.128e-12  
## combined$Raw.Materialfenitized gneiss:combined$Average.Size  
##                                                   9.128e-12  
##          combined$Raw.Materialgranite:combined$Average.Size  
##                                                   9.128e-12  
##        combined$Raw.Materialquartzite:combined$Average.Size  
##                                                   9.128e-12  
##         combined$Raw.Materialrhyolite:combined$Average.Size  
##                                                   9.128e-12
pander(anova(Leeb_AveSize))
## Warning in anova.lm(Leeb_AveSize): ANOVA F-tests on an essentially perfect
## fit are unreliable
Analysis of Variance Table (continued below)
  Df Sum Sq Mean Sq
combined$Raw.Material 5 2701732 540346
combined$Average.Size 1 7.511e-23 7.511e-23
combined\(Raw.Material:combined\)Average.Size 5 6.473e-23 1.295e-23
Residuals 1974 1.438e-19 7.287e-23
  F value Pr(>F)
combined$Raw.Material 7.416e+27 0
combined$Average.Size 1.031 0.3101
combined\(Raw.Material:combined\)Average.Size 0.1777 0.971
Residuals NA NA 
Leeb_AveSize_plot<-ggplot(combined, aes(y=Average.Size , x=Leeb.Hardness , fill=Raw.Material)) + geom_boxplot() + ylab("Average Size") + xlab("Leeb Hardness") + ggtitle("Leeb hardness by Raw material with Average Size")


Leeb_AveSize_plot

leeb hardness ~ raw material * Angle

Leeb_Angle<-lm(combined$Leeb.Hardness ~ combined$Raw.Material *combined$Angle)
Leeb_Angle
## 
## Call:
## lm(formula = combined$Leeb.Hardness ~ combined$Raw.Material * 
##     combined$Angle)
## 
## Coefficients:
##                                          (Intercept)  
##                                            2.848e+02  
##                          combined$Raw.Materialdacite  
##                                           -6.153e+01  
##                combined$Raw.Materialfenitized gneiss  
##                                           -7.376e+01  
##                         combined$Raw.Materialgranite  
##                                           -1.216e+02  
##                       combined$Raw.Materialquartzite  
##                                           -1.058e+02  
##                        combined$Raw.Materialrhyolite  
##                                           -1.008e+02  
##                                       combined$Angle  
##                                            1.159e-13  
##           combined$Raw.Materialdacite:combined$Angle  
##                                           -1.159e-13  
## combined$Raw.Materialfenitized gneiss:combined$Angle  
##                                           -1.159e-13  
##          combined$Raw.Materialgranite:combined$Angle  
##                                           -1.159e-13  
##        combined$Raw.Materialquartzite:combined$Angle  
##                                           -1.159e-13  
##         combined$Raw.Materialrhyolite:combined$Angle  
##                                           -1.159e-13
pander(anova(Leeb_Angle))
## Warning in anova.lm(Leeb_Angle): ANOVA F-tests on an essentially perfect
## fit are unreliable
Analysis of Variance Table (continued below)
  Df Sum Sq Mean Sq F value
combined$Raw.Material 5 2701732 540346 7.41e+27
combined$Angle 1 3.356e-24 3.356e-24 0.04602
combined\(Raw.Material:combined\)Angle 5 2.444e-23 4.887e-24 0.06702
Residuals 1974 1.439e-19 7.292e-23 NA
  Pr(>F)
combined$Raw.Material 0
combined$Angle 0.8302
combined\(Raw.Material:combined\)Angle 0.9969
Residuals NA 
Leeb_Angle_plot<-ggplot(combined, aes(y=Angle , x=Leeb.Hardness , fill=Raw.Material)) + geom_boxplot() + ylab("Angularity") + xlab("Leeb Hardness") + ggtitle("Leeb hardness by Raw material with Angularity")


Leeb_Angle_plot

youngsm ~ raw material * Percent.crystals

youngs_PA<-lm(combined$ymodule ~ combined$Raw.Material * combined$Percent.Area)
youngs_PA
## 
## Call:
## lm(formula = combined$ymodule ~ combined$Raw.Material * combined$Percent.Area)
## 
## Coefficients:
##                                                 (Intercept)  
##                                                   3.830e+00  
##                                 combined$Raw.Materialdacite  
##                                                   2.230e+00  
##                       combined$Raw.Materialfenitized gneiss  
##                                                   1.770e+00  
##                                combined$Raw.Materialgranite  
##                                                   6.200e-01  
##                              combined$Raw.Materialquartzite  
##                                                   1.640e+00  
##                               combined$Raw.Materialrhyolite  
##                                                   7.030e+00  
##                                       combined$Percent.Area  
##                                                   1.646e-15  
##           combined$Raw.Materialdacite:combined$Percent.Area  
##                                                  -1.646e-15  
## combined$Raw.Materialfenitized gneiss:combined$Percent.Area  
##                                                  -1.646e-15  
##          combined$Raw.Materialgranite:combined$Percent.Area  
##                                                  -1.646e-15  
##        combined$Raw.Materialquartzite:combined$Percent.Area  
##                                                  -1.646e-15  
##         combined$Raw.Materialrhyolite:combined$Percent.Area  
##                                                  -1.646e-15
pander(anova(youngs_PA))
## Warning in anova.lm(youngs_PA): ANOVA F-tests on an essentially perfect fit
## are unreliable
Analysis of Variance Table (continued below)
  Df Sum Sq Mean Sq
combined$Raw.Material 5 11222 2244
combined$Percent.Area 1 2.001e-26 2.001e-26
combined\(Raw.Material:combined\)Percent.Area 5 5.752e-26 1.15e-26
Residuals 1974 3.243e-23 1.643e-26
  F value Pr(>F)
combined$Raw.Material 1.366e+29 0
combined$Percent.Area 1.218 0.2699
combined\(Raw.Material:combined\)Percent.Area 0.7003 0.6233
Residuals NA NA 
youngs_PA_plot<-ggplot(combined, aes(y=Percent.Area , x=ymodule , fill=Raw.Material)) + geom_boxplot() + ylab("Percent Area") + xlab("Young's Modulas") + ggtitle("Young's modulas by Raw material with Percent Crystal")


youngs_PA_plot

youngsm ~ raw material * total area

youngs_TotalA<-lm(combined$ymodule ~ combined$Raw.Material *combined$Total.Area)
youngs_TotalA
## 
## Call:
## lm(formula = combined$ymodule ~ combined$Raw.Material * combined$Total.Area)
## 
## Coefficients:
##                                               (Intercept)  
##                                                 3.830e+00  
##                               combined$Raw.Materialdacite  
##                                                 2.230e+00  
##                     combined$Raw.Materialfenitized gneiss  
##                                                 1.770e+00  
##                              combined$Raw.Materialgranite  
##                                                 6.200e-01  
##                            combined$Raw.Materialquartzite  
##                                                 1.640e+00  
##                             combined$Raw.Materialrhyolite  
##                                                 7.030e+00  
##                                       combined$Total.Area  
##                                                 2.229e-15  
##           combined$Raw.Materialdacite:combined$Total.Area  
##                                                -2.229e-15  
## combined$Raw.Materialfenitized gneiss:combined$Total.Area  
##                                                -2.229e-15  
##          combined$Raw.Materialgranite:combined$Total.Area  
##                                                -2.229e-15  
##        combined$Raw.Materialquartzite:combined$Total.Area  
##                                                -2.229e-15  
##         combined$Raw.Materialrhyolite:combined$Total.Area  
##                                                -2.229e-15
pander(anova(youngs_TotalA))
## Warning in anova.lm(youngs_TotalA): ANOVA F-tests on an essentially perfect
## fit are unreliable
Analysis of Variance Table (continued below)
  Df Sum Sq Mean Sq
combined$Raw.Material 5 11222 2244
combined$Total.Area 1 2.001e-26 2.001e-26
combined\(Raw.Material:combined\)Total.Area 5 5.753e-26 1.151e-26
Residuals 1974 3.243e-23 1.643e-26
  F value Pr(>F)
combined$Raw.Material 1.366e+29 0
combined$Total.Area 1.218 0.2699
combined\(Raw.Material:combined\)Total.Area 0.7004 0.6232
Residuals NA NA 
youngs_TotalA_plot<-ggplot(combined, aes(y=Total.Area , x=ymodule , fill=Raw.Material)) + geom_boxplot() + ylab("Total Area") + xlab("Young's Modulas") + ggtitle("Young's modulas by Raw material with Total Area")

youngs_TotalA_plot

youngsm ~ raw material * average size

youngs_AveSize<-lm(combined$ymodule ~ combined$Raw.Material *combined$Average.Size)
youngs_AveSize
## 
## Call:
## lm(formula = combined$ymodule ~ combined$Raw.Material * combined$Average.Size)
## 
## Coefficients:
##                                                 (Intercept)  
##                                                   3.830e+00  
##                                 combined$Raw.Materialdacite  
##                                                   2.230e+00  
##                       combined$Raw.Materialfenitized gneiss  
##                                                   1.770e+00  
##                                combined$Raw.Materialgranite  
##                                                   6.200e-01  
##                              combined$Raw.Materialquartzite  
##                                                   1.640e+00  
##                               combined$Raw.Materialrhyolite  
##                                                   7.030e+00  
##                                       combined$Average.Size  
##                                                   1.234e-13  
##           combined$Raw.Materialdacite:combined$Average.Size  
##                                                  -1.234e-13  
## combined$Raw.Materialfenitized gneiss:combined$Average.Size  
##                                                  -1.234e-13  
##          combined$Raw.Materialgranite:combined$Average.Size  
##                                                  -1.234e-13  
##        combined$Raw.Materialquartzite:combined$Average.Size  
##                                                  -1.234e-13  
##         combined$Raw.Materialrhyolite:combined$Average.Size  
##                                                  -1.234e-13
pander(anova(youngs_AveSize))
## Warning in anova.lm(youngs_AveSize): ANOVA F-tests on an essentially
## perfect fit are unreliable
Analysis of Variance Table (continued below)
  Df Sum Sq Mean Sq
combined$Raw.Material 5 11222 2244
combined$Average.Size 1 1.373e-26 1.373e-26
combined\(Raw.Material:combined\)Average.Size 5 1.183e-26 2.367e-27
Residuals 1974 3.248e-23 1.646e-26
  F value Pr(>F)
combined$Raw.Material 1.364e+29 0
combined$Average.Size 0.8345 0.3611
combined\(Raw.Material:combined\)Average.Size 0.1438 0.9819
Residuals NA NA 
youngs_AveSize_plot<-ggplot(combined, aes(y=Average.Size , x=Leeb.Hardness , fill=Raw.Material)) + geom_boxplot() + ylab("Average Size") + xlab("Young's Modulas") + ggtitle("Young's modulas by Raw material with Average Size")

youngs_AveSize_plot

youngs ~ raw material * Angle

youngs_Angle<-lm(combined$ymodule ~ combined$Raw.Material *combined$Angle)
youngs_Angle
## 
## Call:
## lm(formula = combined$ymodule ~ combined$Raw.Material * combined$Angle)
## 
## Coefficients:
##                                          (Intercept)  
##                                            3.830e+00  
##                          combined$Raw.Materialdacite  
##                                            2.230e+00  
##                combined$Raw.Materialfenitized gneiss  
##                                            1.770e+00  
##                         combined$Raw.Materialgranite  
##                                            6.200e-01  
##                       combined$Raw.Materialquartzite  
##                                            1.640e+00  
##                        combined$Raw.Materialrhyolite  
##                                            7.030e+00  
##                                       combined$Angle  
##                                            1.041e-14  
##           combined$Raw.Materialdacite:combined$Angle  
##                                           -1.041e-14  
## combined$Raw.Materialfenitized gneiss:combined$Angle  
##                                           -1.041e-14  
##          combined$Raw.Materialgranite:combined$Angle  
##                                           -1.041e-14  
##        combined$Raw.Materialquartzite:combined$Angle  
##                                           -1.041e-14  
##         combined$Raw.Materialrhyolite:combined$Angle  
##                                           -1.041e-14
pander(anova(youngs_Angle))
## Warning in anova.lm(youngs_Angle): ANOVA F-tests on an essentially perfect
## fit are unreliable
Analysis of Variance Table (continued below)
  Df Sum Sq Mean Sq F value
combined$Raw.Material 5 11222 2244 1.372e+29
combined$Angle 1 2.708e-26 2.708e-26 1.656
combined\(Raw.Material:combined\)Angle 5 1.972e-25 3.944e-26 2.411
Residuals 1974 3.228e-23 1.635e-26 NA
  Pr(>F)
combined$Raw.Material 0
combined$Angle 0.1983
combined\(Raw.Material:combined\)Angle 0.03438
Residuals NA 
youngs_Angle_plot<-ggplot(combined, aes(y=Angle , x=ymodule , fill=Raw.Material)) + geom_boxplot() + ylab("Angularity") + xlab("Young's Modulas") + ggtitle("Young's modulas by Raw material with Angularity")

youngs_Angle_plot